The answers to the questions
<span>1)What is f(3) if f(x) = -5x3 + 6x2 - x - 4?
a. -74
b. -88
c. 74
d. 182
f(3) = -5(3)^3 + 6(3)^2 - 3 - 4
f(3) = -5(27) + 6(9) - 7
f(3) = -135 + 54 - 7 = -88
(b.)
2)What is f(x + 1) if f(x) = 6x3 - 3x2 + 4x - 9?
a. 6x3 + 12x2 + 4x + 2
b. 6x3 + 3x2 + 8x + 6
c. 6x3 + 21x2 + 20x + 4
d. 6x3 + 15x2 + 16x - 2
f(x + 1) = 6(x + 1)^3 - 3(x + 1)^2 + 4(x + 1) - 9
f(x + 1) = 6(x^3 + 3x^2 + 3x + 1) - 3(x^2 + 2x + 1) + 4x + 4 - 9
f(x + 1) = 6x^3 + 18x^2 + 18x + 6 - 3x^2 - 6x - 3 + 4x + 4 - 9
f(x + 1) = 6x^3 + 15x^2 + 16x - 2
(d.)
3)What is 3[f(x + 2)] if f(x) = x3 + 2x2 - 4?
a. x3 + 8x2 + 20x + 12
b. 3x3 + 12x2 + 18x + 6
c. 3x3 + 24x2 + 60x + 36
d. 3x3 + 18x2 + 24x + 60
f(x + 2) = (x + 2)^3 + 2(x + 2)^2 - 4
f(x + 2) = x^3 + 6x^2 + 12x + 8 + 2x^2 + 8x + 8 - 4
f(x + 2) = x^3 + 8x^2 + 20x + 12
3[f(x + 2)] = 3x^3 + 24x^2 + 60x + 36
(c.)
4)Use synthetic division to determine which of the following is a factor of x3 - 3x2 - 10x + 24.
a. x - 2
b. x - 3
c. x + 4
d. x + 8
2|....1....-3....-10....24
.......1.....-1.....-12....0
(x - 2) works .... (a.)
5)Use synthetic division to determine which of the following is a factor of 2x3 - 13x2 + 17x + 12.
a. x - 2
b. x - 3
c. x + 4
d. x + 6
3|....2....-13....17....12
.......2.....-7.....-4....0
(x - 3) is a factor .... (b.)
6)What is the remainder when (6x3 + 9x2 - 6x + 2) ÷ (x + 2)?
a. -4
b. 0
c. 2
d. 74
-2|....6....9....-6....2
..........6.....-3.....0....2
(c.)
7)What is the remainder when (x3 - x2 - 5x - 3) ÷ (x + 1)?
a. -8
b. 0
c. 2
d. 4
-1|....1....-1....-5....-3
.........1.....-2.....-3....0
(b.)
8)What are the factors of x3 + 2x2 - x - 2?
a. (x - 1)(x + 1)(x - 2) = (x^2 - 1)(x - 2) = x^3 - 2x^2 - x + 2
b. (x - 2)(x + 2)(x - 1)
c. (x - 2)(x + 2)(x + 1)
d. (x - 1)(x + 1)(x + 2) = (x^2 - 1)(x + 2) = x^3 + 2x^2 - x - 2
(d.)
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It would be 30 inches. Hopes this helps.
You will need the fraction on “z” to have a common denominator before you can add the two equations. In this equation the common denominator is 6. So you do not change the left side of the equation however the right side turns into -2/6. Now you can add the z’s together and you can also add the integers together.
After simplification I believe the final answer is 1/2z + 1.
I would maybe wait for someone else to answer so that you can be sure because there are other ways to solve this.
